1. Field of the Invention
The present invention relates to a computer simulating method applied to a semiconductor fabrication process and, in particular, to an impurity diffusion simulating method which takes point-defects into account.
2. Description of the Prior Art
Using a computer, a process simulator calculates and predicts physical amounts and shapes of impurity profiles in a device fabricated by a semiconductor LSI fabrication process including an ion implanting process and an ion diffusing process. When the semiconductor LSI fabrication process is optimized for the maximum electric characteristics using the process simulator, the cost and time for designing LSI chips can be remarkably reduced as compared to the case that many experimental LSI chips are made and tested. In addition, since the process simulator calculates physical amounts of a semiconductor device, it can analyze actions of impurities in the semiconductor device. For details of the process simulator, refer to "Technology of Process Device Simulator (translated title)", by Ryo Dan, Sangyo-Tosho Publishing Company, pp 18-79, Apr. 20, 1990.
In the diffusion simulation for calculating a diffusion process, diffusion equations for individual impurities should be solved to analyze the action of impurities. Point-defects such as interstitial silicon atoms and holes that generate in the ion implanting process interact with implanted impurities. Thus, the impurities acceleratedly diffuse. This phenomenon is explained in "A model for Boron Short Time Annealing After Ion Implantation", IEEE Transactions on Electron Devices, Vol. 40, No. 7, pp. 1215-1222, July, 1993. To simulate such a phenomenon with a computer, diffusion equations for point-defects such as interstitial silicon atoms and holes should be also solved.
On the other hand, the region where a large number of point-defects generate during the ion implanting process become amorphous because the crystal structure of the region deteriorates. When the region is annealed consequently, the amorphous layer is re-crystallized at the beginning. At the interface between the re-crystallized region and the non-amorphous region, point-defects such as interstitial silicon atoms and holes are absorbed, thereby affecting the diffusion of the impurities.
To simulate such a phenomenon on a computer, a term with respect to the absorption of point-defects such as interstitial silicon atoms or holes is included in a diffusion equation. The term with respect to the absorption of point-defects is denoted by R(x, t, T). The term R(x, t, T) is expressed as follows: EQU R(x, t, T)=K(x, T)[C(x, t)-C*(T)] (1),
where x represents an analytic coordinate vector; t represents an analytic time; T represents an analytic temperature; K(x, T) represents the intensity with which point-defects are absorbed; c(x, t) represents a distribution of the concentration of point-defects; and C* (T) represents the concentration of point-defects at the thermal equilibrium.
When the term R(x, t, T) is included in the diffusion equation, to accurately simulate the diffusion of impurities, the intensity K(x, T) should be correctly estimated corresponding to the ion implanting condition.
In a one-dimensional diffusion simulation, as explained in "Modeling high-concentration boron diffusion under amorphization conditions" by Bruno Baccus, Eric Vandenbossche, and Michel Lannoo, Journal of Applied Physics, Vol. 77, No. 11, pp. 5630-5641, June, 1995, the intensity K(x, T) of the absorption of point-defects is expressed by an experiential analytic equation.
In this method, as shown in FIG. 5, using the ion implanting simulator, the distribution in the depth direction of an initial concentration of point-defects (represented by a curve 51) which generate in the ion implanting process is obtained. The distribution is denoted by C.sub.D (x). With the coordinate (depth) x.sub..alpha. where the initial concentration of point-defects is equal to a particular value C.sub.D,.sub..alpha., the intensity K(x, T) (represented by a curve 52) is expressed as follows: ##EQU1## where .alpha.(T) and X.omega. are parameters.
However, in the conventional diffusion simulation, to obtain the intensity by which point-defects are absorbed, the coordinate x.sub..alpha. had to be obtained from the concentration of initial point-defects that generate in the ion implanting process. Thus, it was difficult to extend the diffusion simulation to a two-dimensional or three-dimensional simulation. In addition, since a parameter that can be obtained from the ion implanting condition is only x.sub..alpha., it was difficult to determine a parameter that allows the simulation to be accurately performed in a different ion implanting condition.